-1/4-1/4x=5+2/3x

Solution for -1/4-1/4x=5+2/3x equation:

-1/4-1/4x=5+2/3x

We move all terms to the left:

-1/4-1/4x-(5+2/3x)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 3x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

-1/4x-(2/3x+5)-1/4=0

We get rid of parentheses

-1/4x-2/3x-5-1/4=0

We calculate fractions


(-3x)/192x^2+(-128x)/192x^2+(-3x)/192x^2-5=0

We multiply all the terms by the denominator


(-3x)+(-128x)+(-3x)-5*192x^2=0

Wy multiply elements

-960x^2+(-3x)+(-128x)+(-3x)=0

We get rid of parentheses

-960x^2-3x-128x-3x=0

We add all the numbers together, and all the variables

-960x^2-134x=0

a = -960; b = -134; c = 0;
Δ = b2-4ac
Δ = -1342-4·(-960)·0
Δ = 17956
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{17956}=134$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-134)-134}{2*-960}=\frac{0}{-1920}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-134)+134}{2*-960}=\frac{268}{-1920}
=-67/480
$